Question

a door with width 4.20 m has an arc as shown in diagram .Find: a) radius of the arc B) length of the arc to the nearest cm

Answer 1

Answer:

Ok, we know that the width of the door is 4.20m.

Then, if the arc is at the top of the door, we will have that the diameter of that "half circle" will be equal to the width of the door.

Then the diameter of the arc is 4.20m

And the radius is defined as half of the diameter, so we have:

radius = 4.20m/2 = 2.10m

And we can write this in cm (because the probelm ask for it)

1m = 100cm

then 2.10m = 2.1*100cm = 210cm

Now, we know that the perimeter of a circle is:

P = 2*pi*r

where pi = 3.14

Then the perimeter (or arc) of half a circle will be half of that:

Arc = (2*pi*r)/2 = pi*r

and r = 210cm, pi = 3.14

Arc = 3.14*210cm = 659.4cm